What is Federated Learning?
The analogy is to a federal system of government. In a federation, smaller pieces follow the direction of a higher piece. In federated machine learning, you give your data for processing to the higher machine. The federation in this analogy is a collection of smaller computers. The central computer breaks up your data and gives portions of it to each smaller computer. When those computers are done they return the results and the central computer reassembles them into a single model.
The main idea is distributed processing. Some benefits are:

Cost: it may be cheaper to operate multiple inexpensive computers rather than fewer more expensive computers.
Privacy: if this is sensitive data like healthcare records then perhaps you don't want all of one person's data in a single place where the wrong person can grab it.